Woods got up and down on the third hole of sudden death. The par proved good enough for victory, as Montgomerie's approach shot from a poor lie in a fairway bunker went wet.
Woods became the first man in tournament history to successfully defend his title. The win was his fifth on the European Tour ' not including major championships ' and added another $410,222 to his ever-growing bank account.
Tiger talks about his win
Justin Rose shot 5-under 67 to finish third, at 19-under.
Woods (68) and Montgomerie (69) each finished regulation at 20-under-par 268. Playing only the 443-yard, par-4 18th in the extra session, it took three go-arounds to determine a winner.
Woods made a 10-foot par putt on the 72nd hole to force sudden death. He then lipped out a 12-footer for birdie on the first playoff hole that would have won the tournament.
Both men parred the second extra session, after each missed the green long. Tiger missed chipping in for victory by mere inches.
The third time around, Montgomerie's tee shot landed near the lip in a left fairway bunker. Even with Tiger having again failed to reach the putting surface, Montgomerie went for the green, only to find the water guarding the right-hand side.
Woods chipped to two feet and tapped in for his third Deutsche Bank win (1999).
Showing no signs of intimidation, Montgomerie birdied his first three holes out of the gate Monday. The quick flurry of putting jabs gave the 38-year-old Scot a two-shot lead over his 26-year-old American counterpart. Thats because Woods hit the green in two on the par-5 third, and rolled home the 20-foot eagle putt.
A Montgomerie bogey at the fourth cut the lead to one, where it stayed as both men parred the remaining five holes on the outward half.
Woods tied for the top spot by sticking his approach on the par-4 10th to eight feet and converting the birdie.
Both men birdied the par-5 12th. Tigers second shot went just beyond the putting surface. He chipped three feet past, but made the comebacker to get to 20-under. Montgomerie took the safer route, laying up and sticking his third to four feet.
Woods took his first lead of the tournament on the next hole. He made par on the 178-yard, par-3 13th, while Colin made bogey. Again playing cautiously, Montgomerie rifled his tee shot well right of the water protecting the left of the green. Some 60 feet from the hole, his lag putt rolled dead six feet short. His par save then gave out on the left edge of the cup.
The one-shot differential stayed intact until the par-4 15th. Woods hit his approach shot 20 feet below the hole, while Montgomerie stuck his inside of that. After Tigers birdie effort stubbornly stayed out, Colin's fell in center-cut from 15 feet.
Woods had a chance to regain outright command at the 16th, only to misjudge a 12-footer. Neither man birdied the par-5 17th, leaving the 18th to determine a winner.
Both Woods and Montgomerie missed the green with their approach shots at 18. Montgomerie pitched nicely to gimme range, as Tiger chipped 10 feet past the hole. But as he so often does, Woods nailed the playoff-forcing putt.
'I just said 'You know what, you've been putting well, just stay committed to it - if it goes in, it goes in, if it doesn't, it doesn't,'' said Woods, who narrowly missed countless putts throughout the final round.
Woods has now won all three times he has played this event at St. Leon-Rot. However, it is undecided as to whether or not he will be back to defend his title again next year. The PGA Tour's Verizon Byron Nelson Classic, in which Tiger annually competes, is scheduled the same week in 2003.
'Heidelberg's been great to me, I'd just love to come back,' he said without giving a definitive answer.
For Montgomerie, the defeat was visibly disappointing, but the performance was nonetheless impressive. With his prime in his past, he more than held his own against the present - and future - of golf.
Even more arresting was the fact that Montgomerie, who was using his new caddie for the first time this week, was battling a bad back. He was on twice-daily painkillers throughout the week, and twice needed on-course treatment in round three to alleviate the pain.
In the circumstances, I am very proud to have gone out there and shot 69 today, Montgomerie said. This morning I was about to pull out. I couldnt play. I was very close when I was on the range.
In the play-off, my back was getting far too sore and thats why I was hooking it. But it was good for the TPC of Europe and it was good for the sponsors. It is good for The European Tour to be broadcast this way and in America on The Golf Channel ' it is good to see our tour in this light.'
Both competitors will next head to very familar, and very prosperous venues.
Montgomerie ventures to Surrey, England for the Volvo PGA Championship - a tournament he won 1998-2000 - where he will try to extend his nine-year winning streak on tour.
Woods will travel back Stateside to compete in the Memorial Tournament in Dublin, Ohio, where he is the three-time defending champion.
Final results from the Deutsche Bank-SAP Open